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If gas A has a molecular weight 4 times that of gas B, then the rate of effusion of gas A in relation to gas B through the same hole would be:

A. Equal.
B. 2 times.
C. 16 times.
D. ½ times.

The answer is:

D. ½ times.

Graham's Law of Diffusion and Effusion relates the rate at which a gas diffuses to its molar mass. It is derived from the kinetic molecular theory of gases, and shows mathematically that under constant pressure and temperature the rate at which a gas diffuses and effuses is inversely related to the square root of its molar mass—in other words, the more massive a gas is the slower it will diffuse and effuse, and vice versa.

Since gas A's molecular weight is 4 times greater than that of gas B, it should move √4 times more slowly, or twice as slowly. However, any calculation in this problem is unnecessary; since we know gas A consists of larger molecules, it must move more slowly. Answer choice D is the only choice that reflects this scenario.

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